Which diagram represents the following sets? P=|xis an integer divisible by 2}: Q= (x|xis an odd integer; R =x|xis an integer divisible by 3}

The answer is below

Step-by-step explanation:

An integer is a whole number which is either positive, negative or zero.

Given that:

P=(x | x is an integer divisible by 2}. An integer divisible by 2 can be represented by 2k, where k is an integer, hence:

P = (..., -6, -4, -2, 0, 2, 4, 6, ...)

Q= (x | x is an odd integer). An odd integer can be represented by 2k + 1, where k is an integer, hence:

Q = (..., -5, -3, -1, 1, 3, 5, 7, 9 ...)

R = (x | x is an integer divisible by 3). An integer divisible by 3 can be represented by 3k, where k is an integer, hence:

R = (..., -12, -9, -6, -3, 0, 3, 6, 9, ...)

From the above we can see that Q and P are disjoint set, that is P ∩ Q = 0

But P and R have common numbers (..., -6, 0, 6, 12,...) i.e. P ∩ R ≠ 0

Also Q and R have common numbers (..., -3, 3, 9,...) i.e. Q ∩ R ≠ 0

The question and answer is attached

answer: 20

step-by-step explanation: